High throughput, high color purity, high speed tunable color filters are required to optimize color displays. While there are many color filters known in the art, none simultaneously satisfy all three criteria.
Many color filters are based on the Lyot polarization interference filter (PIF) introduced in 1933 (B. Lyot, Comptes Rendues 197, 1593 [1933]). The building-block for a Lyot polarization interference filter is a stage which consists minimally of a uniaxial retarder bounded by linear polarizers. The optimum configuration requires that the retarder be oriented at .pi./4, and that the analyzing polarizer be parallel or perpendicular to the input polarizer. The transmission function for a single filter stage with parallel polarizers is given by EQU T(.lambda.)=cos.sup.2 ].pi.(m+1).lambda..sub.o /.lambda.] Eq. 1
where .lambda. is the incident free-space wavelength, and the retarder is selected to be m.sup.th order full-wave at the design wavelength, .lambda..sub.o. With crossed polarizers, the analogous sin.sup.2 transmission function is produced.
Typically, filter stages are cascaded using retarders with a common design wavelength and a differing order (m) to produce more selective transmission spectra. The Lyot filter design optimizes filter finesse (ratio of blocking bandwidth to passband width) per number of stages using a geometric relationship of retarder order (m, 2m, 4m . . . ). The classic Lyot filter spectrum is a periodic sinc-function with passband profile determined primarily by the highest order retarder.
Two stages of a Lyot filter can be combined into a single stage using a split-element filter (J. W. Evans, J. Opt. Soc. Am. 39, 229 [1949]). To eliminate the second stage, the birefringent element of the second stage is split in half and these split elements are positioned in series with and on either side of the birefringent element of the first stage. The polarizers are crossed, the center element is oriented parallel to either polarizer, and the split elements are oriented at +.pi./4 and -.pi./4. Wide-field versions of the Lyot filter can also be constructed.
Electronically tunable Lyot-type polarization interference filters using the variable birefringence of homogeneously aligned nematic liquid crystals have been described. Continuous tunability is obtained, but response times of nematic liquid crystals are slow, on the order of 1-100 ms.
Planar aligned smectic liquid crystals, including ferroelectric liquid crystals (FLCs), provide microsecond response times. However, in contrast to nematic liquid crystals, application of an electric field to planar aligned smectic liquid crystals rotates the orientation of the optic axis but does not vary the retardance. Nonetheless, the inventors have previously demonstrated polarization interference color filters using smectic liquid crystals (G. Sharp et al., Opt. Lett. 16, 875 [1991]; K. Johnson and G. Sharp in U.S. Pat. Nos. 5,132,826 [1992], 5,231,521 [1993] and 5,243,455 [1993]).
Although the smectic liquid crystal Lyot filters of the Johnson and Sharp patents are high speed, they cannot be simultaneously both high throughput and high color purity. An aspect of the present invention is the recognition of the tradeoff between throughput and color purity in a Lyot-type design. The transmission of a single stage filter is described in Eq. 1. Differentiating Eq. 1 reveals that the slope of the transition band increases almost linearly with retarder order, which is beneficial to color purity. However, the pass-band-full-width decreases almost inversely with retarder order, decreasing throughput. This tradeoff illustrates that Lyot stages are not optimum for implementing color filters.